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Van Kampen's expansion approach in an opinion formation model

Author

Listed:
  • M. S. de la Lama
  • I. G. Szendro
  • J. R. Iglesias
  • H. S. Wio

Abstract

We analyze a simple opinion formation model consisting of two parties, A and B, and a group I, of undecided agents. We assume that the supporters of parties A and B do not interact among them, but only interact through the group I, and that there is a nonzero probability of a spontaneous change of opinion ( $A \leftrightarrows I$ , $B \leftrightarrows I$ ). From the master equation, and via van Kampen's Ω-expansion approach, we have obtained the “macroscopic” evolution equation, as well as the Fokker-Planck equation governing the fluctuations around the deterministic behavior. Within the same approach, we have also obtained information about the typical relaxation behavior of small perturbations. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006

Suggested Citation

  • M. S. de la Lama & I. G. Szendro & J. R. Iglesias & H. S. Wio, 2006. "Van Kampen's expansion approach in an opinion formation model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 51(3), pages 435-442, June.
    • Handle: RePEc:spr:eurphb:v:51:y:2006:i:3:p:435-442
    DOI: 10.1140/epjb/e2006-00232-8
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    Citations

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    Cited by:

    1. Di Guilmi, C. & Gallegati, M. & Landini, S., 2008. "Economic dynamics with financial fragility and mean-field interaction: A model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3852-3861.
    2. Gimenez, M. Cecilia & Paz García, Ana Pamela & Burgos Paci, Maxi A. & Reinaudi, Luis, 2016. "Range of interaction in an opinion evolution model of ideological self-positioning: Contagion, hesitance and polarization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 320-330.
    3. Agnieszka Kowalska-Styczeń & Krzysztof Malarz, 2020. "Noise induced unanimity and disorder in opinion formation," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-22, July.
    4. Gaudiano, Marcos E. & Revelli, Jorge A., 2019. "Spontaneous emergence of a third position in an opinion formation model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 501-511.
    5. Pedraza, Lucía & Pinasco, Juan Pablo & Semeshenko, Viktoriya & Balenzuela, Pablo, 2023. "Mesoscopic analytical approach in a three state opinion model with continuous internal variable," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    6. Khalil, Nagi & Toral, Raúl, 2019. "The noisy voter model under the influence of contrarians," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 81-92.

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